A framework for statistical modelling of plastic yielding initiated cleavage fracture of structural steels

Abstract

The well established consensus that cleavage fracture is preceded by plastic deformation in structural steels implies that plastic yielding is the threshold stress state for a volume element to incur cleavage fracture. An accurate compliance with this consensus underlies the normalisation of cumulative cleavage fracture probability and the justification of constraint effect on cleavage fracture. These understandings lead to the proposal of a framework for statistical modelling of cleavage fracture in structural steels. The framework takes the spatial microcrack distribution into account to formulate the cumulative failure probability model that allows for a pertinent physical interpretation of Weibull statistics, and derives the fracture probability of an elemental volume in conformity with the yielding condition from a set of commonly adopted microcrack size or strength distributions. Alternative approaches to calibrating model parameters are suggested based on frequency analysis of brittle particles as cleavage initiators and on statistical analysis of cleavage fracture stress. The strict adherence to plastic yielding as a prerequisite to cleavage fracture also reveals the probabilistic nature of notch brittleness and ductile-to-brittle transition behaviour.